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While Facebook and Apple might not look like direct competitors on the surface, that’s not stopping Mark Zuckerberg and Tim Cook from engaging in a war of words with regard to their respective companies’ varying business models.

In a new Time magazine profile, an irritated Zuckerberg is slamming Cook for a letter he wrote regarding Apple’s evolving privacy policies last September. “A few years ago,” wrote Cook at the time, “users of Internet services began to realize that when an online service is free, you’re not the customer. You’re the product.”

While the jab was probably directed at Google, whom Cook has previously called Apple’s chief adversary, Zuckerberg came out swinging.

“A frustration I have is that a lot of people increasingly seem to equate an advertising business model with somehow being out of alignment with your customers,” he toldTime. “I think it’s the most ridiculous concept. What, you think because you’re paying Apple that you’re somehow in alignment with them? If you were in alignment with them, then they’d make their products a lot cheaper!”

Earlier this year, Cook told Charlie Rose that he sees Facebook as a partner rather than a competitor, being that Apple has no foreseeable plans to enter social networking, and that the service is baked into iOS.

Nevertheless, this latest skirmish illustrates that, on a quest for global domination, the fiercely competitive spirit pervading two of Silicon Valley’s most successful companies can even turn allies into enemies.